Projection and slicing theorems in Heisenberg groups

We study the behavior of the Hausdorff dimension of sets in the Heisenberg group Hn, n∈N, with a sub-Riemannian metric under projections onto horizontal and vertical subgroups, and under slicing by translates of vertical subgroups. We formulate almost sure statements in terms of a natural measure on...

Full description

Saved in:
Bibliographic Details
Published in:Advances in mathematics (New York. 1965) 2012-10, Vol.231 (2), p.569-604
Main Authors: Balogh, Zoltán M., Fässler, Katrin, Mattila, Pertti, Tyson, Jeremy T.
Format: Article
Language:English
Subjects:
Hausdorff dimension
Heisenberg group
Isotropic Grassmannian
Potential theory
Projection
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We study the behavior of the Hausdorff dimension of sets in the Heisenberg group Hn, n∈N, with a sub-Riemannian metric under projections onto horizontal and vertical subgroups, and under slicing by translates of vertical subgroups. We formulate almost sure statements in terms of a natural measure on the Grassmannian of isotropic subspaces.
ISSN:0001-8708
1090-2082
DOI:10.1016/j.aim.2012.03.037